Add Cuboid struct

NB: This struct has 7 auto-properties totalling 88 bytes. I feel there may be a way to calculate LocalFront__ given the center point, orientation, and size, but it's been a long day and I cannot think how to optimize this at the moment

X10D/src/Drawing/Cuboid.cs

@@ -0,0 +1,278 @@
+using System.Numerics;
+using X10D.Numerics;
+
+namespace X10D.Drawing;
+
+/// <summary>
+///     Represents a cuboid in 3D space, which uses single-precision floating-point numbers for its coordinates.
+/// </summary>
+public readonly struct Cuboid : IEquatable<Cuboid>
+{
+    /// <summary>
+    ///     Initializes a new instance of the <see cref="Cuboid" /> struct.
+    /// </summary>
+    /// <param name="center">The center point.</param>
+    /// <param name="size">The size.</param>
+    public Cuboid(in Vector3 center, in Vector3 size)
+    {
+        Center = center;
+        Size = size;
+        Orientation = Quaternion.Identity;
+
+        Vector3 halfExtents = Size / 2.0f;
+        LocalFrontTopLeft = new Vector3(-halfExtents.X, halfExtents.Y, -halfExtents.Z);
+        LocalFrontTopRight = new Vector3(halfExtents.X, halfExtents.Y, -halfExtents.Z);
+        LocalFrontBottomLeft = new Vector3(-halfExtents.X, -halfExtents.Y, -halfExtents.Z);
+        LocalFrontBottomRight = new Vector3(halfExtents.X, -halfExtents.Y, -halfExtents.Z);
+    }
+
+    /// <summary>
+    ///     Initializes a new instance of the <see cref="Cuboid" /> struct.
+    /// </summary>
+    /// <param name="center">The center point.</param>
+    /// <param name="size">The size.</param>
+    /// <param name="orientation">The orientation of the cuboid.</param>
+    public Cuboid(in Vector3 center, in Vector3 size, in Quaternion orientation)
+        : this(center, size)
+    {
+        Orientation = orientation;
+
+        Vector3 halfExtents = Size / 2.0f;
+        var localFrontTopLeft = new Vector3(-halfExtents.X, halfExtents.Y, -halfExtents.Z);
+        var localFrontTopRight = new Vector3(halfExtents.X, halfExtents.Y, -halfExtents.Z);
+        var localFrontBottomLeft = new Vector3(-halfExtents.X, -halfExtents.Y, -halfExtents.Z);
+        var localFrontBottomRight = new Vector3(halfExtents.X, -halfExtents.Y, -halfExtents.Z);
+
+        Rotate(
+            orientation,
+            ref localFrontTopLeft,
+            ref localFrontTopRight,
+            ref localFrontBottomLeft,
+            ref localFrontBottomRight);
+
+        LocalFrontTopLeft = localFrontTopLeft;
+    }
+
+    /// <summary>
+    ///     Gets the center point of the cuboid.
+    /// </summary>
+    /// <value>The center point.</value>
+    public Vector3 Center { get; }
+
+    /// <summary>
+    ///     Gets the orientation of this cuboid.
+    /// </summary>
+    /// <value>The orientation.</value>
+    public Quaternion Orientation { get; }
+
+    /// <summary>
+    ///     Gets the size of the cuboid.
+    /// </summary>
+    /// <value>The size.</value>
+    public Vector3 Size { get; }
+
+    /// <summary>
+    ///     Gets the front-top-left corner of the box, in local space.
+    /// </summary>
+    /// <value>The front-top-left corner.</value>
+    public Vector3 LocalFrontTopLeft { get; }
+
+    /// <summary>
+    ///     Gets the front-top-right corner of the box, in local space.
+    /// </summary>
+    /// <value>The front-top-right corner.</value>
+    public Vector3 LocalFrontTopRight { get; }
+
+    /// <summary>
+    ///     Gets the front-bottom-left corner of the box, in local space.
+    /// </summary>
+    /// <value>The front-bottom-left corner.</value>
+    public Vector3 LocalFrontBottomLeft { get; }
+
+    /// <summary>
+    ///     Gets the front-bottom-right corner of the box, in local space.
+    /// </summary>
+    /// <value>The front-bottom-right corner.</value>
+    public Vector3 LocalFrontBottomRight { get; }
+
+    /// <summary>
+    ///     Gets the back-top-left corner of the box, in local space.
+    /// </summary>
+    /// <value>The back-top-left corner.</value>
+    public Vector3 LocalBackTopLeft
+    {
+        get => -LocalFrontBottomRight;
+    }
+
+    /// <summary>
+    ///     Gets the back-top-right corner of the box, in local space.
+    /// </summary>
+    /// <value>The back-top-right corner.</value>
+    public Vector3 LocalBackTopRight
+    {
+        get => -LocalFrontBottomLeft;
+    }
+
+    /// <summary>
+    ///     Gets the back-bottom-left corner of the box, in local space.
+    /// </summary>
+    /// <value>The back-bottom-left corner.</value>
+    public Vector3 LocalBackBottomLeft
+    {
+        get => -LocalFrontTopRight;
+    }
+
+    /// <summary>
+    ///     Gets the back-bottom-right corner of the box, in local space.
+    /// </summary>
+    /// <value>The back-bottom-right corner.</value>
+    public Vector3 LocalBackBottomRight
+    {
+        get => -LocalFrontTopLeft;
+    }
+
+    /// <summary>
+    ///     Gets the front-top-left corner of the box, in world space.
+    /// </summary>
+    /// <value>The front-top-left corner.</value>
+    public Vector3 FrontTopLeft
+    {
+        get => LocalFrontTopLeft + Center;
+    }
+
+    /// <summary>
+    ///     Gets the front-top-right corner of the box, in world space.
+    /// </summary>
+    /// <value>The front-top-right corner.</value>
+    public Vector3 FrontTopRight
+    {
+        get => LocalFrontTopRight + Center;
+    }
+
+    /// <summary>
+    ///     Gets the front-bottom-left corner of the box, in world space.
+    /// </summary>
+    /// <value>The front-bottom-left corner.</value>
+    public Vector3 FrontBottomLeft
+    {
+        get => LocalFrontBottomLeft + Center;
+    }
+
+    /// <summary>
+    ///     Gets the front-bottom-right corner of the box, in world space.
+    /// </summary>
+    /// <value>The front-bottom-right corner.</value>
+    public Vector3 FrontBottomRight
+    {
+        get => LocalFrontBottomRight + Center;
+    }
+
+    /// <summary>
+    ///     Gets the back-bottom-left corner of the box, in world space.
+    /// </summary>
+    /// <value>The back-bottom-left corner.</value>
+    public Vector3 BackTopLeft
+    {
+        get => LocalBackTopLeft + Center;
+    }
+
+    /// <summary>
+    ///     Gets the back-bottom-right corner of the box, in world space.
+    /// </summary>
+    /// <value>The back-bottom-right corner.</value>
+    public Vector3 BackTopRight
+    {
+        get => LocalBackTopRight + Center;
+    }
+
+    /// <summary>
+    ///     Gets the back-bottom-right corner of the box, in world space.
+    /// </summary>
+    /// <value>The back-bottom-right corner.</value>
+    public Vector3 BackBottomLeft
+    {
+        get => LocalBackBottomLeft + Center;
+    }
+
+    /// <summary>
+    ///     Gets the back-bottom-right corner of the box, in world space.
+    /// </summary>
+    /// <value>The back-bottom-right corner.</value>
+    public Vector3 BackBottomRight
+    {
+        get => LocalBackBottomRight + Center;
+    }
+
+    /// <summary>
+    ///     Returns a value indicating whether two instances of <see cref="Cuboid" /> are not equal.
+    /// </summary>
+    /// <param name="left">The first instance.</param>
+    /// <param name="right">The second instance.</param>
+    /// <returns>
+    ///     <see langword="true" /> if <paramref name="left" /> and <paramref name="right" /> are considered not equal; otherwise,
+    ///     <see langword="false" />.
+    /// </returns>
+    public static bool operator ==(Cuboid left, Cuboid right)
+    {
+        return left.Equals(right);
+    }
+
+    /// <summary>
+    ///     Returns a value indicating whether two instances of <see cref="Cuboid" /> are not equal.
+    /// </summary>
+    /// <param name="left">The first instance.</param>
+    /// <param name="right">The second instance.</param>
+    /// <returns>
+    ///     <see langword="true" /> if <paramref name="left" /> and <paramref name="right" /> are considered not equal; otherwise,
+    ///     <see langword="false" />.
+    /// </returns>
+    public static bool operator !=(Cuboid left, Cuboid right)
+    {
+        return !left.Equals(right);
+    }
+
+    private static Vector3 RotatePointAroundPivot(in Vector3 point, in Vector3 pivot, in Quaternion rotation)
+    {
+        Vector3 direction = point - pivot;
+        return pivot + rotation.Multiply(direction);
+    }
+
+    private static void Rotate(
+        in Quaternion orientation,
+        ref Vector3 localFrontTopLeft,
+        ref Vector3 localFrontTopRight,
+        ref Vector3 localFrontBottomLeft,
+        ref Vector3 localFrontBottomRight
+    )
+    {
+        localFrontTopLeft = RotatePointAroundPivot(localFrontTopLeft, Vector3.Zero, orientation);
+        localFrontTopRight = RotatePointAroundPivot(localFrontTopRight, Vector3.Zero, orientation);
+        localFrontBottomLeft = RotatePointAroundPivot(localFrontBottomLeft, Vector3.Zero, orientation);
+        localFrontBottomRight = RotatePointAroundPivot(localFrontBottomRight, Vector3.Zero, orientation);
+    }
+
+    /// <inheritdoc />
+    public override bool Equals(object? obj)
+    {
+        return obj is Cuboid other && Equals(other);
+    }
+
+    /// <summary>
+    ///     Returns a value indicating whether this instance and another instance are equal.
+    /// </summary>
+    /// <param name="other">The instance with which to compare.</param>
+    /// <returns>
+    ///     <see langword="true" /> if this instance and <paramref name="other" /> are considered equal; otherwise,
+    ///     <see langword="false" />.
+    /// </returns>
+    public bool Equals(Cuboid other)
+    {
+        return Center.Equals(other.Center) && Size.Equals(other.Size) && Orientation.Equals(other.Orientation);
+    }
+
+    /// <inheritdoc />
+    public override int GetHashCode()
+    {
+        return HashCode.Combine(Center, Size, LocalFrontTopLeft);
+    }
+}